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Optimal control problem benchmark (Luus) with an integral objective, inequality, and differential constraint. Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. [1]
Control theory is a field of control engineering and applied mathematics that ... Optimal Control and ... Mathematical Control Theory: Deterministic Finite ...
Widely regarded as a milestone in optimal control theory, the significance of the maximum principle lies in the fact that maximizing the Hamiltonian is much easier than the original infinite-dimensional control problem; rather than maximizing over a function space, the problem is converted to a pointwise optimization. [8]
The relationship between these two value functions is called the "Bellman equation". In this approach, the optimal policy in the last time period is specified in advance as a function of the state variable's value at that time, and the resulting optimal value of the objective function is thus expressed in terms of that value of the state variable.
Its solution is the value function of the optimal control problem which, once known, can be used to obtain the optimal control by taking the maximizer (or minimizer) of the Hamiltonian involved in the HJB equation. [2] [3] The equation is a result of the theory of dynamic programming which was pioneered in the 1950s by Richard Bellman and ...
The first paper of Federer and Fleming illustrating their approach to the theory of perimeters based on the theory of currents. with Raymond W. Rishel: Deterministic and stochastic optimal control, Springer, Berlin Heidelberg New York 1975, ISBN 3-540-90155-8 [4] Functions of several variables, Addison Wesley, 1965, Springer, 2nd edition 1977
In control theory, a separation principle, more formally known as a principle of separation of estimation and control, states that under some assumptions the problem of designing an optimal feedback controller for a stochastic system can be solved by designing an optimal observer for the state of the system, which feeds into an optimal deterministic controller for the system.
One of his key contributions is the martingale optimality principle in stochastic control, which characterizes optimal strategies through the martingale property of the value process. [6] In a 1984 paper he introduced the concept of Piecewise deterministic Markov process , [ 7 ] a class of Markov models which have been used in many applications ...